论文标题
在二次单肤色家族中具有局部合理性条件的前观点
Preperiodic points with local rationality conditions in the quadratic unicritical family
论文作者
论文摘要
对于理性数字$ c $，我们提出了一组完全真实的（分别为$ p $ adiC）的三分法，用于二次单政治家庭中的地图$ f_c（x）= x^2+c $。结果，我们将二次多项式$ f_c $与有理参数分类为$ c \ in \ mathbb {q} $，以便$ f_c $只有有限的完全真实（完全是$ p $ - adic，分别为$ p $ - adic）。这些结果依赖于Adelic Fekete-type定理以及$ f_c $的Julia集的动力学。此外，使用[np]中引入的数值标准，我们明确计算完全真实的$ f_c $ -preperiodic点时，当$ c = -1,0，\ frac {1} {5} {5} {5} $和$ \ frac {1} {1} {1} {1} {4} {4} {4} {4}。$
For rational numbers $c$, we present a trichotomy of the set of totally real (totally $p$-adic, respectively) preperiodic points for maps in the quadratic unicritical family $f_c(x)=x^2+c$. As a consequence, we classify quadratic polynomials $f_c$ with rational parameters $c\in\mathbb{Q}$ so that $f_c$ has only finitely many totally real (totally $p$-adic, respectively) preperiodic points. These results rely on an adelic Fekete-type theorem and dynamics of the filled Julia set of $f_c$. Moreover, using a numerical criterion introduced in [NP], we make explicit calculations of the set of totally real $f_c$-preperiodic points when $c=-1,0,\frac{1}{5}$ and $\frac{1}{4}.$
